Biharmonic spline interpolation of GEOS‐3 and SEASAT altimeter data

Abstract

Green functions of the biharmonic operator, in one and two dimensions, are used for minimum curvature interpolation of irregularly spaced data points. The interpolating curve (or surface) is a linear combination of Green functions centered at each data point. The amplitudes of the Green functions are found by solving a linear system of equations. In one (or two) dimensions this technique is equivalent to cubic spline (or bicubic spline) interpolation while in three dimension it corresponds to multiquadric interpolation. Although this new technique is relatively slow, it is more flexible than the spline method since both slopes and values can be used to find a surface. Moreover, noisy data can be fit in a least squares sense by reducing the number of model parameters. These properties are well suited for interpolating irregularly spaced satellite altimeter profiles. The long wavelength radial orbit error is suppressed by differentiating each profile. The shorter wavelength noise is reduced by the least squares fit to nearby profiles. Using this technique with 0.5 million GEOS‐3 and SEASAT data points, it was found that the marine geoid of the Caribbean area is highly correlated with the sea floor topography. This suggests that similar applications, in more remote, areas may reveal new features of the sea floor. Copyright 1987 by the American Geophysical Union.